Title: Recovery of time-dependent coefficients in hyperbolic equations on Riemannian manifolds from partial data.Abstract: In this talk we discuss inverse problems of determining time-dependent coefficients appearing in the wave equation in a compact Riemannian manifold of dimension three or higher. More specifically, we are concerned with the case of conformally transversally anisotropic manifolds, or in […]
Title: Analytic stacks
Title: Properties of log canonical singularities in positive characteristic.Abstract: We will investigate if some well known properties of log canonical singularities over the complex numbers still hold true over perfect fields of positive characteristic and over excellent rings with perfect residue fields. We will discuss both pathological behavior in characteristic p as well as some positive results […]
Title: Covers of P^1 and number fields Abstract: Let $n$ be an integer. Via the Minkowski embedding, an order $mathcal{O}$ in a degree $n$ number field can be seen as a lattice. Similarly, given a degree $n$ cover of $mathbb{P}^1$, the pushforward of the structure sheaf is an interesting rank $n$ vector bundle on $mathbb{P^1}$. […]
Title and abstract TBA
Title: A Hodge-theoretic proof of Hwang's theoremAbstract: I will explain a Hodge-theoretic proof for Hwang's theorem, which says that if the base of a Lagrangian fibration on an irreducible holomorphic symplectic manifold is smooth, then it must be projective space. The result is contained in a joint paper with Ben Bakker from last fall.
Title: On the Harish-Chandra regularity theorem Abstract: The Harish-Chandra regularity theorem roughly says that an invariant eigendistribution on a semisimple Lie group is represented by some locally integrable function. We shall explain the proof of this theorem with an emphasis on the case of SL(2).
Title: Exotic spheres from p-adic cohomology theories.Abstract:Part 1: An n-dimensional exotic sphere is a smooth manifold homeomorphic, but not diffeomorphic, to S^n. I will give a leisurely introduction to the telescope conjecture in stable homotopy theory (recently resolved in joint work with Burklund, Levy, and Schlank), by explaining its implications for the diffeomorphism classification of […]
Title: Finiteness for Hecke algebras of p-adic reductive groups. Abstract: Part 1: Let F be a p-adic field, and G the F-points of a reductive group over F. For any compact open subgroup U of F, one can form the Hecke algebra C of complex valued functions on G, invariant under left and right translation by […]
Title: Singularities in Mixed Characteristic via Alterations.Abstract: Multiplier ideals and test ideals are ways to measure singularities in characteristic zero and p > 0 respectively. In characteristic zero, multiplier ideals are computed by a sufficiently large blowup by comparing the canonical module of the base and the resolution. In characteristic p > 0, test ideals were […]